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Big Ideas Math: Modeling Real Life - Grade 2

Big Ideas Learning, LLC | Second Grade

Alignment: Overall Summary

he instructional materials for Big Ideas Math: Modeling Real Life Grade 2 partially meet the expectations for alignment. The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials partially meet the expectations for Gateway 2, rigor and practice-content connections. The materials partially meet the expectations for rigor by reflecting the balances in the Standards and giving appropriate attention to procedural skill and fluency. The materials partially meet expectations for practice-content connections. The materials identify the practices and attend to the specialized language of mathematics, however, they do not attend to the full intent of the practice standards.

The Report

Gateway One

Focus & Coherence

Meets Expectations

The instructional materials for Big Ideas Math: Modeling Real Life Grade 2 meet the expectations for Gateway 1, focus and coherence. Assessments represent grade-level work, and items that are above grade level can be modified or omitted. Students and teachers using the materials as designed would devote a majority of time to the major work of the grade. The materials are coherent and consistent with the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 2 meet the expectations that the materials do not assess topics from future grade levels. The instructional materials do contain assessment items that assess above grade-level content, but these can be modified or omitted.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

Criterion 1b

The instructional materials for Big Ideas Math: Modeling Real Life Grade 2 meet the expectations for spending a majority of class time on major work of the grade when using the materials as designed. Time spent on the major work was figured using chapters, lessons, and days. Approximately 84% of the time is spent on the major work of the grade.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 2 meet the expectation for spending the majority of class time on the major clusters of each grade. For Grade 2, this includes all clusters within 2.NBT along with 2.OA.A and 2.OA.B, and 2.MD.A and 2.MD.B.

To determine the focus on major work, three perspectives were evaluated: the number of chapters devoted to major work, the number of lessons devoted to major work, and the number of weeks devoted to major work.

The approximate number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 10 out of 15, which is approximately 67% of the instructional time.

The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 88 out of 110 lessons, which is approximately 80% of the instructional time.

The number of days devoted to major work (including assessments and supporting work connected to the major work) is 143 out of 170 days, which is approximately 84% of the instructional time.

A day-level analysis is most representative of the instructional materials because the number of days is not consistent within chapters and lessons. As a result, approximately 84% of the instructional materials focus on the major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 2 meet the expectations that the materials are coherent and consistent with the standards. The materials represent a year of viable content. Teachers using the materials would give their students extensive work in grade-level problems, and the materials describe how the lessons connect with the grade-level standards. However, above grade-level content is present and not identified.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 2 meetexpectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of the connections between supporting work and major work include the following:

Chapter 13, Lesson 1, Show and Grow, Problem 4, connects supporting standard 2.MD.9 to major work 2.OA.2 as students use a chart to determine “How many more students need to choose sneakers so that the number of students who choose sneakers and sandals are equal?”

Chapter 13, Lesson 4, Think and Grow, connects supporting standards 2.MD.10 to major work of 2.OA.2 when students use horizontal and vertical bar graphs with up to four categories. Students answer, “A student chooses an activity that has the same number of votes as crafts and hiking combined. Which activity does the student choose?”

Chapter 14, Lesson 1, Think and Grow, supporting standard 2.MD.8 connects to major work 2.NBT.2 when students count coins and skip-count to count-on in increments. This connection is repeated in Lessons 2, 3, and 4.

Chapter 14, Lesson 5, Think and Grow, connects supporting standard 2.MD.8 to major work 2.NBT.5 when students subtract from 100 to make change for a dollar. Two strategies are outlined: students can count back from 100 by skip-counting the coins backward, or by using a compensation strategy to subtract from 99 instead of 100.

Chapter 14, Lesson 8, Think and Grow, connects supporting standard 2.MD.7 to supporting standard 2.MD.2 when students skip count by 5s to tell time to the nearest five minutes on an analog clock.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

Instructional materials for Big Ideas Math: Modeling Real Life Grade 2 meet expectations that the amount of content designated for one grade-level is viable for one year.

As designed, the instructional materials can be completed in 170 days with each lesson counting as 1 day. The minimum time per class period is 45 minutes, with the recommended time of 60-70 minutes. A pacing guide can be found in the Teachers Guide. Grade Two is divided into 15 Chapters. The 170 days include the following:

110 days of Lessons

15 days of Lesson Opener Activities - Each Chapter begins with a chapter opener.

30 days for “Connect and Grow” Activities - Two days per chapter are dedicated to these activities which include a performance task and chapter practice on one day and centers on the other day.

15 days for Chapter Assessments - Each chapter has a final chapter assessment.

Indicator 1e

Materials are consistent with the progressions in the Standards
i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work
ii. Materials give all students extensive work with grade-level problems
iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 2 partially meets expectations for being consistent with the progressions in the Standards. The presence of above grade-level content distracts from all students engaging with extensive work of the grade.

The Teacher Edition includes a “Progression Through the Grades” chart which outlines each domain and its accompanying clusters, and which chapters address each cluster. Additionally, tables are provided to identify which lessons address specific standards. The beginning of each chapter includes an overview table “Progressions Through the Grades” that shows the content from the previous and future grade levels, and “Laurie’s Overview” where the math in the chapter is explained and connected to prior and future work of the grade. For example:

The "Progression Through the Grades chart" states: Grade 1 “Use properties of addition and subtraction as strategies. Fluently add and subtract within 10. Determine the unknown number to complete addition and subtraction equations.” Grade 2 “Determine whether the number of objects in a group is even or odd. Write an addition equation to model even numbers. Fluently add and subtract within 20. Use repeated addition to count the number of objects. “ Grade 3 “Identify addition and multiplication patterns. Use strategies to fluently add and subtract within 1000. Fluently multiply and divide within 100. Understand that factors show the number of equal groups and the size of equal groups.”

The instructional materials develop according to the grade-by-grade progressions. For example, in the Teacher Edition, Chapter 9, Lesson 6 addresses 2.NBT.7:

Explore and Grow: “Model to solve. Make a quick sketch of your model. 327+458= ?”

Think and Grow and Apply and Grow: “272+154 = ?” includes a place value chart to model drawings of base ten blocks and includes a problem written vertically with place value identified and a box to show regrouping.

Practice: additional practice problems are included.

Throughout the instructional materials, above grade-level content is present. This content is not identified as above grade-level, and distracts students from engaging with extensive work with grade-level mathematics to meet the full intent of grade-level standards. For example:

Chapter 15, Lesson 5, “Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.” (2.G.2) There are 3 lessons (Chapter 15, Lessons 6, 7, and 8) that students “Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.” (2.G.3)

Chapter 12, Lesson 1, students connect the ruler they have just practiced with to the number line to solve addition, subtraction, and compare problems. (2.MD.6) In Lesson 2, students practice with bar models. This is a missed opportunity to help students build a mental model of number lines to add and subtract which is key to working with number lines in grade 3. (3.NF.2)

The portion of the lessons titled “Connect and Extend Learning” includes a section “Prior Skills” that clearly identifies prior-grade content. For example,

Teacher Edition, Chapter 3, Laurie’s Notes, Preparing to Teach, “In this lesson, students work with the familiar hundreds chart to add groups of ten. In Grade 1, students used the chart to count on from a decade number, now we expand to a starting addend that is not a decade number. Students will transfer between working on the hundreds chart to representing their counting on an open number line.”

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards
i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings.
ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 2 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, and they provide problems and activities that connect two or more clusters in a domain or two or more domains when the connections are natural and important.

Chapter 1, Lesson 3, Apply and Grow, “Determine the total number of objects in equal groups.” Students look at circled items and fill in blanks (ex. ____ groups of ____). Then the student writes the repeated addition equation to match the pictures and solve the equation. (2.OA.C)

Chapter 3, Lesson 3, Explore and Grow, the Learning Target is visibly shaped by the cluster heading 2.NBT.B. The directions state, “How can you use a model to solve 37+15 (problem is written vertically).” The problem has a place value chart labeled tens and ones for the student to use to model the problem with base-ten blocks.

Chapter 4, Lesson 4, Explore and Grow, the Learning Target states, “Use regrouping when needed to add.” Students make a sketch of base-ten blocks in a place value chart to find “38 + 24”. (2.NBT.C)

Chapter 7, Lesson 1, Explore and Grow, the Learning Target states, “Identify groups of tens as hundreds.” Students identify how many unit cubes and rods are in a flat. (2.NBT.B)

Chapter 7, Lesson 5, Explore and Grow, the Learning Target states, “Represent numbers in different ways.” Show and Grow students “show 261 two ways”, and “show 345 two ways”. (2.NBT.A)

Chapter 11, Lesson 3, Show and Grow, students draw an object based on the estimated measurement of another object. For example, “The piece of celery is about 10 centimeters long. Draw a carrot that is about 5 centimeters long.” (2.MD.A)

Examples of problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, include:

Chapter 2, Lesson 1, Show and Grow, connects representing and solving problems involving addition and subtraction (2.OA.A) with adding and subtracting within 20 (2.OA.B). For example, Question 11, “There are 13 race cars. 6 of them have numbers. The rest do not. How many race cars do not have numbers?”

Chapter 3, Lesson 1, Think and Grow, relates addition and subtraction to length as a strategy (2.MD.B) with using place value understanding and properties of operations to add and subtract (2.NBT.B) For example, “Write an equation that matches the number line.” The number line shows starting at 43 and counting by tens three times in order to reach 73.

In Chapter 9, Lesson 2, Explore and Grow, students “Show how to skip count by tens five time on the number line.” The number line starts with the number 154. Students make 5 hops of 10 on the number line. Then students finish an equation “154 + ____ = ____ (154 + 50 = 204)”. This connects understanding place value (2.NBT.A) with using place value understanding and properties of operations to add and subtract (2.NBT.B).

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

The instructional materials for Big Ideas Math: Modeling Real Life Grade 2 partially meet the expectations for rigor and mathematical practices. The materials partially meet the expectations for rigor by reflecting the balances in the Standards and giving appropriate attention to procedural skill and fluency. The materials partially meet the expectations for practice-content connections, they identify the Standards for Mathematical Practices, and attend to the specialized language of mathematics, but do not attend to the full intent of each practice standard.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 2 partially meet the expectations for rigor and balance. The instructional materials give appropriate attention to procedural skill and fluency, and the materials address the three aspects with balance, not always treating them separately and not always together.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 2 partially meets expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Cluster 2.NBT.A addresses understanding place value of ones, tens and hundreds. Students read, write, and count to 1,000. Students skip-count by 5s, 10s, and 100s. Student use base-ten numerals, number names, and expanded form when writing and reading numbers in addressing conceptual understanding. Students also compare two three-digit numbers. Examples from Chapters 7, 8, 9, 10, 11, and 14 include:

Chapter 7, Lesson 3, Show and Grow, Numbers 4 and 5, students are asked to circle the values of the underlined digit. There are two possible answers for each problem, one in standard form, and one written with ones, tens or hundreds. Example, “434: student must circle both '4' and '4 ones'.”

Chapter 8, Lesson 5, Explore and Grow, students represent a three-digit number with a base-ten block drawing, then circle the greater number. Students answer, “How do you know which number is greater?” Students refer to place value for a correct answer. Example, “472 is greater than 439 because the hundreds are the same, and 7 tens is greater than 3 tens.” This develops the understanding of 2.NBT.4 (Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.).

Cluster 2.NBT.B addresses understanding place value of ones, tens and hundreds and properties of operations to add and subtract. Topics 5-11 explore ways to demonstrate conceptual understanding of addition and subtraction using properties of operations as well as place value within 1000. Examples from Chapters 2-6, 9, 10, and 11 include:

Chapter 9, Lesson 2, Explore and Grow, students use a number line to add two 3-digit numbers. Students are encouraged to use the diagram to skip-count by place value (100s, 10s, 1s). This develops the understanding of 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.).

Chapter 10, Lesson 3, Explore and Grow, students use a number line to subtract two 3-digit numbers. Students are encouraged to use the diagram to skip-count backward by place value (100s, 10s, 1s). This develops the understanding of 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.).

Chapter 11, Lesson 3, Show and Grow, students draw an object based on estimated measurement of another object. Example, “The piece of celery is about 10 centimeters long. Draw a carrot that is about 5 centimeters long.” This develops the understanding of 2.MD.3 (Estimate lengths using units of inches, feet, centimeters, and meters.).

Some opportunities for students to demonstrate conceptual understanding independently are evident, the instructional materials do not always provide students opportunities to independently demonstrate conceptual understanding throughout the grade-level. Within the Apply and Grow and Homework and Practice sections, students have limited opportunities to independently demonstrate conceptual understanding.

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 2 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The instructional materials have opportunities to develop procedural skills and fluency throughout the grade-level especially where called for by 2.OA.2, Fluently add and subtract within 20; and 2.NBT.5, Fluently add and subtract within 100. For example:

Chapter 1, Lesson 2, Show and Grow, supports addition within 20 because the equations used to support even and odd numbers also reinforce addition within 20. “Students are shown a rectangular array model that shows 7 and students have to record an equation 7=___ + ___ and tell whether the number is even or odd.” (2.OA.2)

Chapter 2, Lesson 5, Think and Grow, “There are 13 backpacks in your classroom. 9 are taken. How many backpacks are left?” Students use the number line to count backwards (2.OA.2).

Chapter 3, Lesson 4, Think and Grow, students decompose and recompose with addends. For example, “34 + 25 = ___” students decompose 25 to “2 tens and 5 ones”. They merge the 2 tens with 34 to arrive at 54. Students then add in the 5 ones to get the answer of 59 (2.NBT.5).

Chapter 4, Lesson 1, Think and Grow, students are introduced to tables for tens and ones to add their addends. For example, “33 + 43 = ___”. Students list 3 and 4 in the tens table and 3 and 3 in the ones portion of the table. Students then add each column to arrive at 7 tens and 6 ones (2.NBT.5).

Chapter 4, Lesson 3, Think and Grow, students record their base ten blocks in a tens and ones chart with regrouping of ones to make a ten. Then students record the blocks as numbers in the tens and ones chart. For example, “29 + 34 = ___” (2.NBT.5).

Chapter 5, Lesson 1, Show and Grow, students use the hundreds chart and open number line to subtract. Example 1, “70 - 50 =___”. Example 2, “33 - 20 = ___” (2.NBT.5).

The instructional materials present opportunities for students to independently demonstrate procedural skill and fluency, for example:

Chapter 14, Lesson 5, Show and Grow, students solve money problems to practice two-digit addition and subtraction. “You buy a banana for 25 cents and an orange for 45 cents. You pay with $1. What is your change?”

Games are included in Chapters 1-7 that are presented both in the Student Edition and online. The games allow students the opportunity to practice procedural fluency with addition and subtraction within 100 (2.NBT.5). The games include: Joey Jump, Three in A Row: Addition and Subtraction, and Solve and Cover: Addition and Subtraction.

Online games include Joey’s Jump, Chapter 2 (facts to 10 but done all as addition even though he goes in reverse order); Three in a Row 3, Chapter 3 (fluency with a limited number of addition facts to get 3 in a row); Solve and Cover, Chapter 4 (fluency with addition facts)

Three in a Row 3, Chapter 5 (fluency with a limited number of subtraction facts to get 3 in a row).

Solve and Cover, Chapter 6 (fluency with subtraction facts).

Chapter 5, Center 4, Mystery Hundred Chart, gives students the opportunity to practice their procedural fluency subtracting within 100. “Have students solve each subtraction equation, then color the differences in the given color on their Hundred Chart. If solved and colored correctly, students should have created a giraffe.” Correlating with 2.NBT.5, Fluently add and subtract within 100.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The instructional materials for Big Ideas Math: Modeling Real Life Grade 2 partially meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

The instructional materials present opportunities for students to engage in routine applications of grade-level mathematics. For example:

Chapter 2 Lesson 1, Show and Grow, includes three “put together/take apart addend unknown” problems. For example, Problem 11, “There are 13 race cars. 6 of them have numbers. The rest do not. How many race cars do not have numbers?” Students write both an addition and a subtraction equation to solve the problem.

Chapter 2, Lesson 8, Apply and Grow, students use information from a tally chart to answer a “compare with differences unknown” problem. “Using information from the chart: ‘How many fewer students have hazel eyes than brown eyes?’”

Chapter 4, Lesson 8, Show and Grow, contains an “start unknown” problem. “You have some stickers. Your friend gives you 32 more stickers. Now you have 58. How many stickers did you have to start?” Students write an equation to solve.

Chapter 5, Lesson 2, Show and Grow, students use an open number line to solve subtraction word problems. Both are “compare/difference unknown” problems. “Your classroom has 26 desks and 38 chairs. How many more chairs are there?”

The instructional materials present few opportunities for students to engage in non-routine applications of the mathematics. Most problems are routine application representing the common addition and subtraction situations in Grade 2.

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 2 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All standards are treated the same way even though the standard may be conceptual in nature, but always procedural and application are embedded.

The instructional materials present opportunities for students to engage in each aspect of rigor within each lesson, as well as multiple aspects of rigor. For example:

Chapter 1, Lesson 4, students develop conceptual understanding of repeated addition. Laurie’s Notes, Dig In (Circle Time), students use 12 counters to make a rectangular shape. They identify how many rows and the number in each row. Students look at each other’s rectangles and notice the different rectangle possibilities. Teacher records each rectangle description with an equation “4 rows of 3: 3 + 3 + 3 + 3 = 12.”

Chapter 2, Lesson 8, Apply and Grow, students work on procedural skills and fluency to add and subtract within 20 for a total of 43 problems.

Chapter 5, Lesson 6, Show and Grow, Problem 12, “There are 36 cars in a parking lot. Some of them leave. There are 31 left. How many cars leave the parking lot?”

Students have opportunities to engage in multiple aspects of rigor. For example:

Chapter 3, Lesson 1, Think and Grow: Modeling Real Life, “A clown has 62 balloons. She uses 40 of them to make balloon animals. How many balloons are left?” Laurie’s Notes, Dig In (Circle Time), “Tell your partner what you notices about counting back by tens on the hundreds chart. Listen for the tens digit changes and the ones digit remains the same, and the numbers are in the same column.”

Chapter 9, Lesson 5, Show and Grow, Problem 17, “A clothing store has some shirts on hangers. There are 214 shirts on shelves. The store has 356 shirts in all. How many shirts are on hangers?

Chapter 13, Lesson 2, Modeling Real Life, Problem 3, Students “use the picture graph” on favorite after-school activities. Categories include: “Play outside, Video games, Watch TV, Read.” “Do students like to play video games and read or play outside and watch tv? More students like to ____ and ____.”

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials for Big Ideas Math: Modeling Real Life Grade 2 partially meet the expectations for practice-content connections. The materials identify the practice standards and explicitly attend to the specialized language of mathematics. However, the materials do not attend to the full meaning of each practice standard.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 2 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade-level.

The Standards for Mathematical Practice (MP) are identified in the digital Teacher's Edition on page vi. The guidance for teachers includes the title of the MP, how each MP helps students, where in the materials the MP can be found, and how it correlated to the student materials using capitalized terms. For example, MP2 states, "Reason abstractly and quantitatively.

"Visual problem-solving models help students create a coherent representation of the problem.

Explore and Grows allow students to investigate concepts to understand the REASONING behind the rules.

Exercises encourage students to apply NUMBER SENSE and explain and justify their REASONING."

The MPs are explicitly identified in Laurie’s Notes in each lesson, and are connected to grade-level problems within the lesson. For example:

Chapter 3, Lesson 1, Laurie’s Notes, students use an open number line to count on multiples of 10. MP2, “Together as a class solve Exercise 1. ‘The start number on our line is 70. To add 30, how many jumps of 10 are we going to make?”

Chapter 11, Lesson 2, students measure objects around the room in either centimeters or meters. Students must choose a ruler or meter stick to measure. This is an example MP5 enriching the content, but the lesson is not labeled as using MP5.

The MPs are identified in the digital Student Dashboard under Student Resources, Standards for Mathematical Practice. This link takes you to the same information found in the Teacher Edition. In the Student Edition, MPs are noted with an abbreviated title, for example, “MP Number Sense” or “MP Structure.” Examples include:

Chapter 7, Lesson 3, Practice, Problem 7, “MP Structure. Write each number in the correct circle.” One circle is labeled “5 in the tens place”. The second circle is labeled “2 in the hundreds place”. The numbers provided are: 152, 215, 452, 205, 650.

Chapter 12, Lesson 3, Apply and Grow: Practice, Problem 5, “MP Number Sense. The path to school is 181 meters long in all. How long is the missing part of the path?” The path is show in three segments: 74 meters, 86 meters, and ? meters.

There are instances where MPs are over or under-identified in the materials. For example:

MP2 is identified in most lessons.

MP5 is under identified. For example, in Chapter 11, Lesson 2, students measure objects around the room in either centimeters or meters. Students must choose a ruler or meter stick to measure. This is an example MP5 enriching the content, but the lesson is not labeled as using MP5.

MP8 is under-identified as students generalize addition and subtraction as traditional algorithms.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 2 do not meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

The instructional materials present few opportunities for student to engage with the full intent of MP1: Make sense of problems and persevere in solving them; MP5: Choose appropriate tools strategically; and MP7: Look for and make use of structure. In addition, there are limited opportunities for students to engage in MP5 and MP8 throughout the materials, so they cannot engage with the full intent of the practice.

MP1 is identified in the instructional materials, however, there are few instances were students need to persevere to find a solution. In many cases where problems are labeled MP1, the directions tell students how to solve the problem. For example:

Student Edition, Chapter 1, Lesson 5, Apply and Grow, Practice, Problem 5, “MP Number Sense.” “Use the array to complete the equation. ___ + 6 = 12”. Students are given an array of 2 rows with 6 squares in each row.

Chapter 3, Lesson 7, Think and Grow, students solve, “You have 8 acorns and find 9 more. Your friend has 32 acorns. How many acorns do you and your friend have together? Circle what you know. Step 1: Find how many acorns you have. Underline what you need to find. Step 2: Find the sum of your acorns and your friend’s acorns.” In the Teacher Edition, Laurie’s Notes, provide questions for teachers: “What does 17 represent? Why are you adding 17 and 32?”

Chapter 12, End of Chapter Practice, Problem 4, “MP Number Sense". "A car tire is 61 centimeters tall. A truck tire is 84 centimeters tall. A monster truck tire is 167 centimeters tall. Which sentences are true?” Three choices are given with two being correct.

MP4 is identified in the materials, however, models are given to students. In addition, throughout the materials in Laurie’s Notes there is guidance labeled “Model” without explicit connections to MP4. For example:

Chapter 3, Lesson 1, Laurie’s Notes, Think and Grow, is listed as using MP4. “Ask for the start number, mark it on the open number line. Elicit responses for ‘What should we do next?’ As students suggest next step, draw + 10 arcs and the corresponding values for each jump. Write the total for you on the left side blank and the total for the friend on the right side to correspond blank and the total for the friend on the right side to correspond to the order in the final question. Comparing using < or > and identify the person who has more.”

Chapter 7, Lesson 2, Think and Grow, Laurie’s Notes: “Model: Descartes tells us what number is in each place value. How can we use this to tell what the number is? How does this help us to write the number?”

MP5 is identified a total of four times throughout the entire curriculum. While the Dynamic Student Edition includes tools for students, the instructional materials present few opportunities for students to choose their own tool, therefore, the full meaning of MP5 is not being attended to. MP 5 is not found in Chapters 1, 3, 4, 5, 6, 7, 9, 12, 13, and 14.

Chapter 10, Lesson 8, Laurie’s Notes, Think and Grow, “Students can be confused about where the answer is when they use a number line. Student A is looking at how much to jump to get to 245. Student B is looking at where they land on the number line after they subtracted 100. It is important for students to recognize the difference.” Students are directed to use a number line rather than choose a tool that works best for them.

Chapter 11, Lesson 5, Laurie’s Notes, Exercise 8, “MP Choose Tools.” The problem states, “Would you measure the length of the playground with an inch ruler or a yardstick? Explain.” The guidance for teachers states, “Students explain which tools is best for measuring the length of a playground. This is a good problem to focus on for students who want to use an Inch Ruler for all their measurements. Using an inch ruler here would mean laying the ruler end-to-end for the entire playground. Using a yardstick would go much faster.”

MP8 is identified a total of five times throughout the entire curriculum. These identified instances do not use words “regularity”, “repeated”, or “reasoning” in places where MP8 is identified. In the Teacher Edition, page vi describes MP8, “students are continually encouraged to check for reasonableness in their solutions." MP8 is not found in Chapters 4, 6, 7, 8, 9, 11, 12, 13, and 14.

Chapter 10, Lesson 4, Explore and Grow, MP8 “What if the problem were 243 - 198? How could we make this an easier problem to subtract? Pause. Ask a few students to share how they think about compensation with three-digit numbers.”

Chapter 1, Lesson 4, Think and Grow, MP8 Look for and Express Regularity in Repeated Reasoning, “In Exercise 3, what do you notice about the rectangle? Listen for square. ‘What is special in a square array?’ Same number of rows and columns.”

Chapter 2, Lesson 6, Think and Grow, “Encourage students to use the model to discuss the whole and parts and how the missing part can be found in subtraction. This reasoning will help students as subtraction becomes more difficult. The strategy of adding to subtract also shows the inverse relationship of addition and subtraction.”

In Chapter 8, Lesson 3, Apply and Grow, Question 12, MP Repeated Reasoning. “Use place value to describe each pattern. 540, 640, 740, … and 310, 320, 330, … ” The answer students are to give is “The hundreds digit increases by 1” and “The tens digit increases by 1.” This does not meet the full intent of MP8 as the digit either increases by 1 ten or it increases by 1 hundred.

The following is an example where materials label “Logic” as a MP7. Question 7 is labeled “MP Logic.” The problem states, “Find the missing digits. 32 + 2__ + 24 = 63 + __5.” There is not an MP “Logic.”

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

Chapter 11, Lesson 1, Apply and Grow: Practice, You be the Teacher, Problem 7, “Newton says the ribbon is about 14 centimeters long. Is he correct? Explain.” Students are presented with a picture of a centimeter ruler and the ribbon placed at 2cm.

Chapter 13, Lesson 6, Show and Grow, “8 people measure the length of a playground. The line plot shows the measured lengths. How long do you think the playground is? Explain. Dig Deeper: Why are the measurements different?” The line plot shows one measure of 48 and 49 cm, and 6 measures of 50 cm.

The instructional materials present few opportunities for students to construct arguments. MP3 is not identified in the student materials. In most instances, students are asked to explain how they know, but they do not always need to construct a mathematical argument. For example:

Chapter 6, Lesson 5, Explore and Grow, “Write an equation shown by each model. How are the equations related? Explain how you can check whether 24-13 = 11 is correct.” The models show 26 + ? = 43, and 26 + 17 = ?.

Chapter 8, Lesson 3, Think and Grow: Modeling Real Life, Problem 14, “Dig Deeper! There are 410 people at a show. 8 more rows of seats get filled. Not there are 490 people. How many people can sit in each row? Explain how you solved.”

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The materials identify MP3 in the Teacher Edition. Laurie’s Notes sometimes include guidance to support teachers to engage students in constructing viable arguments and analyzing the arguments of others. For example:

Chapter 2, Lesson 4, Laurie’s Notes, Think and Grow, MP3, “Look at Exercise 3. Does it matter which addend you decide to make into a ten? Have students compare ways they made a ten.”

Chapter 3, Lesson 5, MP3 is identified and states, “‘Circle the cubes you’ll move and draw an arrow to where they’ll go. Tell a partner which cubes you decided to move and why.’ Show each method with students assisting throughout.”

Chapter 3, Lesson 6, Laurie’s Notes, Think and Grow, “Choose one of the exercises. Explain to your partner the strategy we used. Tell whether or not you think this was the best strategy or if another strategy would work better. Encourage partners to ask why?”

Chapter 4, Lesson 3, Laurie’s Notes, Think and Grow, MP3 example states, “Some students may use mental math to solve. In Exercise 5 they may say, ‘I know 45 + 40 = 85, so 45 + 39 is just one less or 84.’ In Exercise 6, they may reason, ‘Adding just the tens I know I have $70. I only need $3 more to raise more money than my friend.’ Other students should critique this reasoning.”

Chapter 5, Lesson 4, Laurie’s Notes, Think and Grow, MP3, “Ask volunteers to explain why their partner numbers for 8 would be helpful in answering 23 - 8. Listen for I can subtract 3 to get to 20 and then 5 more to get to 15. There may be students who think subtracting 4 and then 4 more is easy. Most will think that subtracting from a decade number is easiest since it is related to fluency with partner numbers for 10.”

Chapter 9, Lesson 6, Laurie’s Notes, Think and Grow, MP3 example states, “Some students may use mental math to solve Exercise 5 and say, ‘I know 300 + 300 = 600. 328 is 28 more than 300 and 219 is more than 28 away from 300 so when I add the two numbers together I won’t get 600.' Other students should critique this reasoning.”

Chapter 13, Lesson 4, Laurie’s Notes, Think and Grow, MP3, “Ask different students to share which way they prefer to organize data and answer questions, bar graph or picture graph, and why.”

There are instances where MP3 is identified and guidance is provided to teachers to engage students to explain, rather than construct an argument or analyze the argument of others. For example:

Chapter 1, Lesson 5, Laurie’s Notes, Think and Grow, MP3 example states, “Have a student reread the problem. ‘Can we answer the question? Does your answer make sense?'” These questions do not engage students in constructing arguments or analyzing the arguments of others.

Chapter 4, Lesson 3, Laurie’s Notes, Think and Grow, MP3, “How do students know this is 41? You want to hear an explanation of exchanging or replacing 10 units for 1 rod.”

Chapter 6, Lesson 2, Laurie’s Notes, Think and Grow, MP3, “How can you tell if you need to regroup?” "Students may answer, 'I look at how many ones I have in the first number. If the second number is less, I don’t have to regroup.'"

Chapter 10, Lesson 1, Laurie’s Notes, Think and Grow, MP3, “Have students explain how this subtraction problem is different from most of the problems they have been doing. Have them share how they can find the new tens and hundreds digits after subtracting 10.”

Chapter 12, Lesson 2, Laurie’s Notes, Think and Grow, MP3, “Who can explain how they wrote the subtraction equation?”

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.

In the Instructional Resources Grade 2, vocabulary cards are provided for each chapter. Each Chapter begins with a Vocabulary Lesson, vocabulary activity, and vocabulary cards. Practice opportunities on the computer are available for vocabulary by chapter.

The following are examples where the materials use precise vocabulary with the students:

Chapter 2, Vocabulary Review, students review previous vocabulary terms “number line”, “count on”, and “count back” by filling out a graphic organizer. Then students match new terms to pictures. In the teacher materials, titled “Vocabulary”, the materials state, “Have students lay out their vocabulary cards in front of them with the picture side facing up. Say the word on the vocabulary card, show the word, and describe the picture definition to students. Have students find the corresponding card. Have students take turns showing the card and telling a partner about the word and its picture definition.”

The materials use the vocabulary regularly in directions for the students. For example, Chapter 2, Lesson 1, “Find the sum. Then change the order of the addends.”

Chapter 2, Lesson 5, Laurie’s Notes, Think and Grow, MP6 is identified and states, “Encourage students to reread the problem using their equation to check for reasonableness.” This has students combine MP8 (reasonableness) with MP6 (precision).

Chapter 4, Lesson 5, Laurie’s Notes, Think and Grow, the materials encourage students to share their thinking as they solve the problem aloud. It also gives direction to the teacher to listen for students attending to precision when justifying their answer, “Do they (students) use appropriate language in describing how 12 is regrouped?”

Chapter 9, Lesson 7, Laurie’s Notes, Think and Grow, Attend to Precision, “When students finish, discuss the different approaches or strategies that may have been used to find the sum. Ask volunteers if they can explain a strategy that is different from how they found the sum. Pay attention to language and reference to place value.”

Chapter 10, Lesson 6, Laurie’s Notes, Think and Grow, Attend to Precision, “When students finish, discuss the different approaches that may have been used to find the difference. Did anyone make a quick sketch? Did any student draw in the vertical lines? Did all students show the regrouping in the same way? Pay attention to language and reference to place value."

Gateway Three

Usability

Not Rated

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.

N/A

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

N/A

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

N/A

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

N/A

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

N/A

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

N/A

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

N/A

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

N/A

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

N/A

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

N/A

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

Criterion 3m - 3q

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

N/A

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.

N/A

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

N/A

Indicator 3p

Materials offer ongoing formative and summative assessments:

N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.

N/A

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

N/A

Indicator 3q

Materials encourage students to monitor their own progress.

N/A

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

N/A

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.

N/A

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

N/A

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

N/A

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.

N/A

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.

N/A

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.

N/A

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

N/A

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

N/A

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

N/A

Indicator 3ac

Materials can be easily customized for individual learners.
i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

N/A

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

Indicator Specific item that reviewers look for in materials.

Criterion Combination of all of the individual indicators for a single focus area.

Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.

Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

Focus and Coherence

Rigor and Mathematical Practices

Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

K-8 Math

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.